What is your characters life situation? I personally would travel since I have never been to foreign lands. I would do it with my family and friends so that I can spend time simultaneously with the people I love.
Make it dark and have your main go on a killing spree. Maybe a list of famous people and have your main take them all out.
This is from a personal point of view and please read all the way and don't stop half-point or it is going to sound really wrong: When I was preggars, the doctors told me one if not both of my daughters had a 98% chance of dying (twin mom here). It rocked me. So based on this, I did what I wanted for the sake of my daughters. Their needs came first. So here I was sitting in between my mom and sister (both matriarchs of their households) listening to them arguing loudly over what I should and shouldn't do blah blah blah. It was a funny moment for me. Here I was with this heart-ripping if I lost one daughter and possibly soul rendering experience if I lost both my daughters (momma bear? Psht, I make bears look like they are negligent), and my family felt like they could make this decision for me. After thirty minutes of this I calmly stated, "Look, what I do, what I choose is my decision, and at the end of the day I want to know that I did everything I could." That was the closest I got to a speech. I think the same thing goes when you have a limited amount time left. "I want to be happy with the choices I made before I kick the bucket." *By the way my daughters are badass and made it. Perfectly normal girls who can give Alexander The Great a run not only for his money, but for his empire as well..... Lol.
Stop cleaning up the mess I leave in my room every day. Stop caring about my diet. Travel. A lot. Watch all the stupid reality shows I'm supposed to be too smart and rebellious to watch. Overthrow the government with a communist revolution. Go down into the history books. Travel some more. Get published. Travel more. Die.
personally I'v found that this is never fulfilled to the depths it can be. For instance, in the movie the bucket list Morgan freeman and some other dude spend the other dude's money, going all over the world to cross off everything on Morgan freeman's bucket list as he only has a short time left to live. it's great that the person gets to do whatever they wish, but subsequently their life turns into nothing more than a hollowed existence. Depending on the setting of your story, you should have the character do something that makes a true change in the world. If it's world war 2 and I find out I have a year left to live, I'd consider going rambo die hard and shooting hitler. If it's when trump is president, I'd consider the same thing yet again, though it doesn't have to be something that extreme. Spend your time at an orphanage and give the kids something. If I'm rich donate the money or start a charity to give people a better life.
Well, a year to live, literally, is 365-ish days. Why not let the character seek to chase a bucket list item... for 365 people? That is a bit different. Perhaps that is another book. I dub it "365 Buckets." The twist could be at the death of said character, when 365 buckets with candles are laid around the burial plot, or something.